"Introduction". In: Fiber-Optic Communication Systems

6.2. SEMICONDUCTOR OPTICAL AMPLIFIERS 235

Figure 6.5: Amplifier gain versus signal wavelength for a semiconductor optical amplifier whose
facets are coated to reduce reflectivity to about 0.04%. (After Ref. [3];©c1987 IEEE; reprinted
with permission.)

whereΓis the confinement factor,σgis the differential gain,Vis the active volume,
andN 0 is the value ofNrequired at transparency. The gain has been reduced byΓto
account for spreading of the waveguide mode outside the gain region of SOAs. The
carrier populationNchanges with the injection currentIand the signal powerPas
indicated in Eq. (3.5.2). Expressing the photon number in terms of the optical power,
this equation can be written as

dN

dt

=

I

q

−

N

τc

−

σg(N−N 0 )

σmhν

P, (6.2.6)

whereτcis the carrier lifetime andσmis the cross-sectional area of the waveguide
mode. In the case of a CW beam, or pulses much longer thanτc, the steady-state
value ofNcan be obtained by settingdN/dt=0 in Eq. (6.2.6). When the solution is
substituted in Eq. (6.2.5), the optical gain is found to saturate as

g=

g 0

1 +P/Ps

, (6.2.7)

where the small-signal gaing 0 is given by

g 0 =(Γσg/V)(Iτc/q−N 0 ), (6.2.8)

and the saturation powerPsis defined as

Ps=hνσm/(σgτc). (6.2.9)

A comparison of Eqs. (6.1.1) and (6.2.7) shows that the SOA gain saturates in the same
way as that for a two-level system. Thus, the output saturation powerPouts is obtained